Problem: Simplify the following expression: $ r = \dfrac{6t + 5}{-9t} + 4 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-9t}{-9t}$ $ \dfrac{-4}{1} \times \dfrac{-9t}{-9t} = \dfrac{36t}{-9t} $ Therefore $ r = \dfrac{6t + 5}{-9t} - \dfrac{36t}{-9t} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{6t + 5 - 36t }{-9t} $ Distribute the negative sign: $r = \dfrac{6t + 5 - 36t}{-9t}$ $r = \dfrac{-30t + 5}{-9t}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{30t - 5}{9t}$